“When, by the direction of the United States Government, ten or eleven years ago, the narrowest part of the Gulf-stream was examined, figures were obtained which shut out all idea of its ever reaching our shores as a heat-bearing current. In the narrowest part, certainly not more than from 250 to 300 cubic miles of water pass per diem. Six months afterwards that water reaches the banks of Newfoundland, and nine or twelve months afterwards the coast of England, by which time it is popularly supposed to cover an area of 1,500,000 square miles. The proportion of the water that passes through the Gulf of Florida will not make a layer of water more than 6 inches thick per diem over such a space. Every one knows how soon a cup of tea cools; and yet it is commonly imagined that a film of only a few inches in depth, after the lapse of so long a time, has an effect upon our climate. There is no need for calculations; the thing is self-evident.”[92]
About five years ago, Mr. Findlay objected to the conclusions which I had arrived at regarding the enormous heating-power of the Gulf-stream on the ground that I had over-estimated the volume of the stream. He stated that its volume was only about the half of what I had estimated it to be. To obviate this objection, I subsequently reduced the volume to one-half of my former estimate.[93] But taking the volume at this low estimate, it was nevertheless found that the quantity of heat conveyed into the Atlantic through the Straits of Florida by means of the stream was equal to about one-fourth of all the heat received from the sun by the Atlantic from the latitude of the Strait of Florida up to the Arctic Circle.
Mr. Findlay, in his paper read before the British Association, affirmed that the volume of the stream is somewhere from 294 to 333 cubic miles per day; but in his remarks at the close of Dr. Carpenter’s address, he stated it to be not greater than from 250 to 300 cubic miles per day. I am unable to reconcile any of those figures with the data from which he appears to have derived them. In his paper to the British Association, he remarks that “the Gulf-stream at its outset is not more than 39½ miles wide, and 1,200 feet deep.” From all attainable data, he computes the mean annual rate of motion to be 65·4 miles per day; but as the rate decreases with the depth, the mean velocity of the whole mass does not exceed 49·4 miles per day. When he speaks of the mean velocity of the Gulf-stream being so and so, he must refer to the mean velocity at some particular place. This is evident; for the mean velocity entirely depends upon the sectional area of the stream. The place where the mean velocity is 49·4 miles per day must be the place where it is 39½ miles broad and 1,200 feet deep; for he is here endeavouring to show us how small the volume of the stream actually is. Now, unless the mean velocity refers to the place where he gives us the breadth and depth of the stream, his figures have no bearing on the point in question. But a stream 39½ miles broad and 1,200 feet deep has a sectional area of 8·97 square miles, and this, with a mean velocity of 49·4 miles per day, will give 443 cubic miles of water. The amount, according to my estimate, is 459 cubic miles per day; it therefore exceeds Mr. Findlay’s estimate by only 16 cubic miles.
Mr. Findlay does not, as far as I know, consider that I have over-estimated the mean temperature of the stream. He states[94] that between Sand Key and Havana the Gulf-stream is about 1,200 feet deep, and that it does not reach the summit of a submarine ridge, which he states has a temperature of 60°. It is evident, then, that the bottom of the stream has a temperature of at least 60°, which is within 5° of what I regard as the mean temperature of the mass. But the surface of the stream is at least 17° above this mean. Now, when we consider that it is at the upper parts of the stream, the place where the temperature is so much above 65°, that the motion is greatest, it is evident that the mean temperature of the entire moving mass must, according to Mr. Findlay, be considerably over 65°. It therefore follows, according to his own data, that the Gulf-stream conveys into the Atlantic an amount of heat equal to one-fourth of all the heat which the Atlantic, from the latitude of the Straits of Florida up to the arctic regions, derives from the sun.
But it must be borne in mind that although the mean temperature of the cross section should be below 65°, it does not therefore follow that the mean temperature of the water flowing through this cross section must be below that temperature, for it is perfectly obvious that the mean temperature of the mass of water flowing through the cross section in a given time must be much higher than that of the cross section itself. The reason is very simple. It is in the upper half of the section where the high temperature exists; but as the velocity of the stream is much greater in its upper than in its lower half, the greater portion of the water passing through this cross section is water of high temperature.
But even supposing we were to halve Mr. Findlay’s own estimate, and assume that the volume of the stream is equal to only 222 cubic miles of water per day instead of 443, still the amount of heat conveyed would be equal to one-eighth part of the heat received from the sun by the Atlantic. But would not the withdrawal of an amount of heat equal to one-eighth of that received from the sun greatly affect the climate of the Atlantic? Supposing we take the mean temperature of the Atlantic at, say, 56°; this will make its temperature 295° above that of space. Extinguish the sun and stop the Gulf-stream, and the temperature ought to sink 295°. How far, then, ought the temperature to sink, supposing the sun to remain and the Gulf-stream to stop? Would not the withdrawal of the stream cause the temperature to sink some 30°? Of course, if the Gulf-stream were withdrawn and everything else were to remain the same, the temperature of the Atlantic would not actually remain 30° lower than at present; for heat would flow in from all sides and partly make up for the loss of the stream. But nevertheless 30° represents the amount of temperature maintained by means of the heat from the stream. And this, be it observed, is taking the volume of the stream at a lower estimate than even Mr. Findlay himself would be willing to admit. Mr. Findlay says that, by the time the Gulf-stream reaches the shores of England, it is supposed to cover a space of 1,500,000 square miles. “The proportion of water that passes through the Straits of Florida will not make,” according to him, “a layer of water more than 6 inches thick per diem over such a space.” But a layer of water 6 inches thick cooling 25° will give out 579,000 foot-pounds of heat per square foot. If, therefore, the Gulf-stream, as he asserts, supplies 6 inches per day to that area, then every square foot of the area gives off per day 579,000 foot-pounds of heat. The amount of heat received from the sun per square foot in latitude 55°, which is not much above the mean latitude of Great Britain, is 1,047,730 foot-pounds per day, taking, of course, the mean of the whole year; consequently this layer of water gives out an amount of heat equal to more than one-half of all that is received from the sun. But assuming that the stream should leave the half of its heat on the American shores and carry to the shores of Britain only 12½° of heat, still we should have 289,500 foot-pounds per square foot, which notwithstanding is more than equal to one-fourth of that received from the sun. If an amount of heat so enormous cannot affect climate, what can?
I shall just allude to one other erroneous notion which prevails in regard to the Gulf-stream; but it is an error which I by no means attribute either to Mr. Findlay or to Dr. Carpenter. The error to which I refer is that of supposing that when the Gulf-stream widens out to hundreds of miles, as it does before it reaches our shores, its depth must on this account be much less than when it issues from the Gulf of Mexico. Although the stream may be hundreds of miles in breadth, there is no necessity why it should be only 6 inches, or 6 feet, or 60 feet, or even 600 feet in depth. It may just as likely be 6,000 feet deep as 6 inches.
The Reason why such Diversity of Opinion prevails in Regard to Ocean-currents.—In conclusion I venture to remark that more than nine-tenths of all the error and uncertainty which prevail, both in regard to the cause of ocean-currents and to their influence on climate, is due, not, as is generally supposed, to the intrinsic difficulties of the subject, but rather to the defective methods which have hitherto been employed in its investigation—that is, in not treating the subject according to the rigid methods adopted in other departments of physics. What I most particularly allude to is the disregard paid to the modern method of determining the amount of effects in absolute measure.
But let me not be misunderstood on this point. I by no means suppose that the absolute quantity is the thing always required for its own sake. It is in most cases required simply as a means to an end; and very often that end is the knowledge of the relative quantity. Take, for example, the Gulf-stream. Suppose the question is asked, to what extent does the heat conveyed by that stream influence the climate of the North Atlantic? In order to the proper answering of this question, the principal thing required is to know what proportion the amount of heat conveyed by the stream into the Atlantic bears to that received from the sun by that area. We want the relative proportions of these two quantities. But how are we to obtain them? We can only do so by determining first the absolute quantity of each. We must first measure each before we can know how much the one is greater than the other, or, in other words, before we can know their relative proportions. We have the means of determining the absolute amount of heat received from the sun by a given area at any latitude with tolerable accuracy; but the same cannot be done with equal accuracy in regard to the amount of heat conveyed by the Gulf-stream, because the volume and mean temperature of the stream are not known with certainty. Nevertheless we have sufficient data to enable us to fix upon such a maximum and minimum value to these quantities as will induce us to admit that the truth must lie somewhere between them. In order to give full justice to those who maintain that the Gulf-stream exercises but little influence on climate, and to put an end to all further objections as to the uncertainty of my data, I shall take a minimum to which none of them surely can reasonably object, viz. that the volume of the stream is not over 230 cubic miles per day, and the heat conveyed per pound of water not over 12½ units. Calculating from these data, we find that the amount of heat carried into the North Atlantic is equal to one-sixteenth of all the heat received from the sun by that area. There are, I presume, few who will not admit that the actual proportion is much higher than this, probably as high as 1 to 3, or 1 to 4. But, who, without adopting the method I have pursued, could ever have come to the conclusion that the proportion was even 1 to 16? He might have guessed it to be 1 to 100 or 1 to 1000, but he never would have guessed it to be 1 to 16. Hence the reason why the great influence of the Gulf-stream as a heating agent has been so much under-estimated.
The same remarks apply to the gravitation theory of the cause of currents. Viewed simply as a theory it looks very reasonable. There is no one acquainted with physics but will admit that the tendency of the difference of temperature between the equator and the poles is to cause a surface current from the equator towards the poles, and an under current from the poles to the equator. But before we can prove that this tendency does actually produce such currents, another question must be settled, viz. is this force sufficiently great to produce the required motion? Now when we apply the method to which I refer, and determine the absolute amount of the force resulting from the difference of specific gravity, we discover that not to be the powerful agent which the advocates of the gravitation theory suppose, but a force so infinitesimal as not to be worthy of being taken into account when considering the causes by which currents are produced.